Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

<p>Validation of <span class="nowrap"><svg height="12.3328pt" id="M327" style="vertical-align:-3.31848pt" version="1.1" viewbox="-0.0498162 -9.01432 20.668 12.3328" width="20.668pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M714 664L702 678C677 661 651 638 627 626C588 607 568 607 547 607C524 607 496 619 461 638C391 673 360 687 319 687C215 687 144 611 144 536S191 410 271 410C339 410 379 452 412 517L394 526C361 473 326 440 273 440C209 440 185 482 185 534S237 635 301 635C329 635 366 621 403 601C456 572 487 557 527 557C532 557 540 557 547 558C427 454 384 369 336 292C189 231 53 149 53 45C53 9 77 -15 110 -15C127 -15 146 -11 166 -4C260 31 369 152 443 298L550 339C495 254 446 155 446 77C446 21 481 -12 533 -12C594 -12 659 42 735 134L714 147C642 63 586 18 547 18C528 18 513 32 513 53C513 111 593 253 687 387C835 446 991 527 991 637C991 673 965 687 934 687C874 687 752 597 612 422L579 379C540 364 503 356 464 340C536 484 606 581 696 650L714 664ZM958 635C958 559 851 493 720 434C805 554 896 657 934 657C950 657 958 650 958 635ZM307 241C253 147 171 15 110 15C98 18 86 24 86 44C86 120 179 182 307 241Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.961,3.132)"><path d="M417 653C377 677 335 687 290 687C171 687 83 622 83 541C83 462 150 415 250 398C231 363 224 320 224 292C224 212 282 165 361 165C409 165 455 180 499 209L500 208C439 89 369 16 246 16C183 16 127 48 122 79H124C131 68 141 66 153 66C181 66 197 90 197 117C197 142 173 164 146 164C111 164 87 134 87 95C87 39 157 -15 256 -15C421 -15 531 60 586 209C606 264 620 298 652 330L637 346C520 239 440 195 368 195C324 195 302 225 302 262C302 293 311 343 343 390C542 390 740 489 740 593C740 642 693 669 637 669C526 669 359 580 263 428C175 440 124 482 124 541C124 602 193 657 297 657C332 657 369 652 408 635L417 653ZM699 590C699 512 532 420 361 420C425 535 557 632 642 632C673 632 699 618 699 590Z"></path></g></svg>-</span>graph Kannan mapping.</p>

Discrete Dynamics in Nature and Society

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Figure 4

Figure 4: Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam 