Fixed point results for generalized F-contractions in modular metric and fuzzy metric spaces

Abstract

The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contraction in modular metric space and investigate the existence of fixed points for such contractions. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and fixed point theorems for contractions involving integral inequalities. Moreover, we deduce new fixed point results in triangular fuzzy metric spaces and provide some examples to illustrate the usability of the obtained results.

Contraction Mappings and Applications

“…0 such that for all x, y ∈ X , ðÞ , then T has a fixed point in X . For more in this direction, see, [28][29][30][31]. Here, we give the concept of multivalued α-F-weak-contractions and prove some fixed point results.…”

Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

“…Recall that T : X → 2 X is monotone increasing if T ⪯ T for all , ∈ X, for which ⪯ (see [8]). There are many applications in differential and integral equations of monotone mappings in ordered metric spaces (see [15,[24][25][26] and references therein). In this section, from Theorems 7-13, we derive the following new results in partially ordered metric spaces and give an example to integral equations.…”

Fixed point theorems for generalized multivalued nonlinear F -contractions

“…We say that T is monotone increasing, if T y T z, for all y, z ∈ X , for which y z. There are many applications in differential and integral equations of monotone mappings in ordered metric spaces (see [2,7,16,17] and references therein). In this section, from Sections 2 and 3, we derive the following new results in partially ordered metric spaces.…”