Abstract
Under the <svg style="vertical-align:-3.56265pt;width:9.7250004px;" id="M1" height="16.3125" version="1.1" viewBox="0 0 9.7250004 16.3125" width="9.7250004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.813)"><path id="x1D719" d="M542 242q0 -106 -80 -176.5t-192 -72.5l-55 -251l-6 -3q-18 7 -28 38t1 91l23 124q-85 16 -133.5 72.5t-48.5 137.5q0 95 62.5 159.5t166.5 97.5l14 -31q-77 -32 -115 -82.5t-38 -128.5q0 -63 31.5 -107t74.5 -59l125 597l56 43l16 -10l-40 -168q-9 -40 3 -45
q77 -33 120 -85.5t43 -140.5zM469 232q0 67 -37 115t-77 62l-76 -370q89 -4 139.5 52.5t50.5 140.5z" /></g> </svg>-contraction conditions, we prove common fixed point theorems for self-mappings in the space <svg style="vertical-align:-2.3205pt;width:55.049999px;" id="M2" height="15.0875" version="1.1" viewBox="0 0 55.049999 15.0875" width="55.049999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D49E" d="M449 645l-12 -19q-55 31 -136 31q-52 0 -103 -17t-85.5 -54.5t-34.5 -84.5q0 -60 41.5 -96.5t109.5 -43.5q81 125 216 216q137 92 240 92q46 0 71 -19.5t25 -55.5q0 -60 -67 -123q-66 -63 -177 -105q-109 -42 -225 -42q-69 -100 -69 -199q0 -49 31.5 -79.5t85.5 -30.5
q79 0 141 50q61 49 61 108q0 35 -20 54.5t-51 19.5q-53 0 -103 -53q-47 -52 -55 -131l-22 2q0 91 58 158t139 67q55 0 86.5 -26.5t31.5 -76.5q0 -81 -96 -148q-78 -54 -174 -54q-86 0 -141 46q-56 47 -56 127q0 81 48 171q-72 12 -121 55t-49 115q0 75 71 131q72 57 185 57
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q36 0 61 15q36 21 57 63t21 91q0 70 -46 95q-24 -6 -49 -6q-38 0 -47 19q-158 -326 -414 -326q-76 0 -125 35q-48 36 -48 87q0 31 17 51.5t42 20.5q22 0 36.5 -13.5t14.5 -34.5t-11.5 -34.5t-31.5 -13.5q-23 0 -30 12h-2q0 -28 35 -54q34 -25 85 -25q94 0 161 53
q67 54 151 202q70 124 134 203q64 77 141 127q-82 56 -210 56q-91 0 -178 -32q-85 -32 -139 -92q-55 -61 -55 -137q0 -48 30 -77t81 -29q84 0 144 75q61 76 65 196h20q0 -125 -64 -213t-170 -88q-65 0 -106 38t-41 105q0 64 39 120.5t103 91.5q134 72 269 72q144 0 244 -67
q40 22 87 40zM841 485q0 54 -40 95q-43 -36 -79 -89t-83 -143q7 4 23 4q25 0 55 -14q60 4 92 49q32 44 32 98z" /></g><g transform="matrix(.017,-0,0,-.017,29.759,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,35.641,12.138)"><path id="x1D44B" d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" /></g><g transform="matrix(.017,-0,0,-.017,49.104,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g> </svg> of the bounded closed sets in the complete stationary fuzzy metric space with the <svg style="vertical-align:-3.27605pt;width:27.799999px;" id="M3" height="15.25" version="1.1" viewBox="0 0 27.799999 15.25" width="27.799999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28
h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g> <g transform="matrix(.012,-0,0,-.012,14.975,15.187)"><path id="x1D440" d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" /></g> </svg>-fuzzy metric for the bounded closed sets.
Highlights
It is well known that the Hausdorff metric is very important concept in general topology and analysis, and many authors have expansively developed the theory of fuzzy sets and application
Let (X, M, ∗) be a complete stationary fuzzy metric space and let {fn}∞ n=1 be a sequence of self-mappings of CB(X)
We have established the completeness of CB(X) with respect to the completeness of the stationary fuzzy metric space X
Summary
It is well known that the Hausdorff metric is very important concept in general topology and analysis, and many authors have expansively developed the theory of fuzzy sets and application (see [1,2,3,4,5,6,7,8,9,10,11]). In [20], Rodrıguez-Lopez and Romaguera introduced and discussed a suitable notion for the Hausdorff fuzzy metric of a given fuzzy metric space (in the sense of George and Veeramani) on the set of its nonempty compact subsets. Many researches have been done on the fixed point theory in the space of compact fuzzy sets equipped with the supremum metric [1, 16, 31,32,33,34,35,36,37,38]. We will prove some common fixed point theorems for self-mappings in the space CB(X)
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