In this paper, we establish some upper bounds of the numerical radius of a bounded linear operator <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2064009pt" id="M1" height="8.8423pt" version="1.1" viewBox="-0.0498162 -8.6359 6.25863 8.8423" width="6.25863pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-84" d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"/></g></svg> defined on a complex Hilbert space with polar decomposition <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.399pt" style="vertical-align:-2.15067pt" id="M2" height="11.439pt" version="1.1" viewBox="-0.0498162 -9.28833 17.399 11.439"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-84"/></g><g transform="matrix(.013,0,0,-0.013,9.768,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="16.505pt" style="vertical-align:-2.15067pt" height="11.439pt" version="1.1" viewBox="20.9811838 -9.28833 16.505 11.439"><g transform="matrix(.013,0,0,-0.013,21.031,0)"><path id="g113-86" d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"/></g><g transform="matrix(.013,0,0,-0.013,34.117,0)"><path id="g113-9" d="M162 -163V703H101V-163H162Z"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="13.419pt" style="vertical-align:-2.15067pt" height="11.439pt" version="1.1" viewBox="41.1181838 -9.28833 13.419 11.439"><g transform="matrix(.013,0,0,-0.013,41.168,0)"><use xlink:href="#g113-84"/></g><g transform="matrix(.013,0,0,-0.013,50.936,0)"><use xlink:href="#g113-9"/></g></svg><span class="ipunc"></span></span>, involving generalized Aluthge transform. These bounds generalize some bounds of the numerical radius existing in the literature. Moreover, we consider particular cases of generalized Aluthge transform and give some examples where some upper bounds of numerical radius are computed and analyzed for certain operators.

Tao Yan

Javariya Hyder

Muhammad Saeed Akram

Ghulam Farid

Kamsing Nonlaopon

On Numerical Radius Bounds Involving Generalized Aluthge Transform

The aim of this paper is to establish the Ulam stability of the Caputo-Fabrizio fractional differential equation with integral boundary condition. We also present the existence and uniqueness results of the solution for the Caputo-Fabrizio fractional differential equation by Krasnoselskii&#x2019;s fixed point theorem and Banach fixed point theorem. Some examples are provided to illustrate our theorems.

Shuyi Wang

The Ulam Stability of Fractional Differential Equation with the Caputo-Fabrizio Derivative

This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.

Khadijeh Sadri

Hossein Aminikhah

Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis

This paper is aimed at establishing some unique common fixed point theorems in complex-valued <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M2" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-99"/></g></svg>-</span>metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M3" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-99"/></g></svg>-</span>metric space can be used in other types of integral operators.

Rashad A. R. Bantan

Saif Ur Rehman

Shahid Mehmood

Waleed Almutiry

Amani Abdullah Alahmadi

Mohammed Elgarhy

An Approach of Integral Equations in Complex-Valued <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063999pt" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-99" d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" /></g></svg>-Metric Space Using Commuting Self-Maps

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M3" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 4.9929 6.1673" width="4.9929pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-116"/></g></svg>-</span>distance spaces under <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="13.937pt" style="vertical-align:-3.42947pt" id="M4" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 13.937 12.7178"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><use xlink:href="#g113-230"/></g><g transform="matrix(.013,0,0,-0.013,10.973,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="10.31pt" style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="16.0661838 -9.28833 10.31 12.7178"><g transform="matrix(.013,0,0,-0.013,16.116,0)"><use xlink:href="#g113-243"/></g><g transform="matrix(.013,0,0,-0.013,23.462,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="13.236pt" style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="28.556183800000003 -9.28833 13.236 12.7178"><g transform="matrix(.013,0,0,-0.013,28.606,0)"><use xlink:href="#g113-245"/></g><g transform="matrix(.013,0,0,-0.013,37.11,0)"><use xlink:href="#g113-42"/></g></svg>-</span></span>type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

Maliha Rashid

Amna Kalsoom

Abdul Ghaffar

Mustafa Inc

Ndolane Sene

A Multiple Fixed Point Result for <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-3.42947pt" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 41.8425 12.7178" width="41.8425pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" /></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path id="g113-230" d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" /></g><g transform="matrix(.013,0,0,-0.013,10.973,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" /></g><g transform="matrix(.013,0,0,-0.013,16.116,0)"><path id="g113-243" d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z" /></g><g transform="matrix(.013,0,0,-0.013,23.462,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" /></g><g transform="matrix(.013,0,0,-0.013,28.606,0)"><path id="g113-245" d="M642 419L635 448C586 435 552 411 532 392C518 379 509 351 496 304C484 260 462 196 445 150C424 93 388 40 314 30L413 508L406 510L344 491L257 36C205 46 175 84 175 169C175 195 180 241 185 277C189 304 190 331 190 358C190 413 175 448 141 448C111 448 69 429 23 373L30 347C51 365 68 375 81 375C93 375 108 368 108 327C108 307 104 268 101 239C98 211 95 180 95 155C95 33 159 -8 248 -14L213 -186C206 -220 221 -254 230 -261L261 -230L306 -11C339 -4 366 6 389 20C431 46 473 87 503 155C533 224 557 286 571 325C586 367 606 393 642 419Z" /></g><g transform="matrix(.013,0,0,-0.013,37.11,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" /></g></svg>-Type Contractions in the Partially Ordered <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063904pt" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 4.9929 6.1673" width="4.9929pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-116" d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" /></g></svg>-Distance Spaces with an Application

The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

Mohammed Kbiri Alaoui

F. M. Alharbi

Shamsullah Zaland

[Retracted] Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.

Tzu-Chien Yin

Nawab Hussain

A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities

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<p><em>Journal of Function Spaces</em> publishes research on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines.</p>


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<p>Chief Editor, Dr Ragusa, is a full professor of mathematical analysis at University of Catania, Italy. Her research interests include partial differential equations and real analysis.</p>


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Journal of Function Spaces - Table of contents 2022

title

Journal of Function Spaces publishes research on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines.

Journal of Function Spaces