Conventional mathematical tools which require all inferences to be exact, are not always sufficient to handle imprecisions in a wide variety of practical fields. Thus, among various developments in fuzzy mathematics, enormous efforts have been in process to produce new fuzzy analogues of the classical fixed point results and their various applications. Following this line in this paper, a new type of set-valued mapping whose range set lies in a family of soft sets is examined. To this effect, we introduce a few fixed point theorems which are generalizations of several significant fixed point results of point-to-point and point-to-set valued mappings in the comparable literature. Some of these particular cases are noted and analyzed. Moreover, nontrivial examples are provided to support the assumptions of our main results. تفاصيل المقالة

‎The aim of this paper is to introduce the concept of multi-valued contraction that combine a renowned \'{C}iri\'{c}-type contraction and Caristi-type contractions in the framework of metric spaces‎. ‎The existence of fixed points for such contractions equipped with some suitable hypotheses are proved and some analogues of the fixed point theorems presented herein are deduced as corollaries‎. ‎Moreover‎, ‎an example is given to illustrate the validity of obtained main result‎. تفاصيل المقالة

In this paper, two novel extensions of Banach and Meir-Keeler fixed point theorems for $L$-fuzzy set-valued map defined on a complete metric space are presented by using new general contractive conditions under suitable assumptions. In the case when the $L$-fuzzy set-valued map is reduced to its crisp counterparts, our obtained concepts herein generalize several significant fixed point theorems of point-to-point and point-to-set valued mappings in the comparable literature. We provide non-trivial examples to validate the hypotheses of our results. تفاصيل المقالة