Existence of Unique Solution of Urysohn and Fredholm Integral Equations in Complex Double Controlled Metric Type Spaces

<div>Convergence behavior of <span class="nowrap"><svg height="9.39034pt" id="M289" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 14.6098 9.39034" width="14.6098pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M583 333C583 398 556 448 506 448C465 448 403 428 328 383C238 329 167 252 115 162C110 186 106 208 106 232C106 311 133 374 194 424L176 448C81 390 29 315 29 201C29 144 44 95 69 62C43 -14 29 -91 29 -141C29 -196 67 -261 115 -261C181 -261 246 -214 246 -126C246 -76 228 -51 192 -8C163 27 152 43 138 86C174 178 224 250 294 305C361 358 425 392 461 392C479 392 496 372 496 316C496 199 462 38 386 38C366 38 340 66 324 108C322 114 307 116 298 111C277 99 270 84 270 65C270 29 304 -12 358 -12C384 -12 423 3 469 41C535 96 583 223 583 333ZM198 -142C198 -181 173 -205 149 -205C122 -205 94 -174 94 -121C94 -92 101 -42 114 6C157 -37 198 -83 198 -142Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.878,0)"><path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

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Figure 4

Figure 4: Existence of Unique Solution of Urysohn and Fredholm Integral Equations in Complex Double Controlled Metric Type Spaces 