Geraghty-type theorems in modular metric spaces with an application to partial differential equation

Best proximity point theorems in 1/2−modular metric spaces

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

Common Fixed Point Theorems of Integral Type in Modular Spaces

Best Proximity Point Theorems for Generalized Almost Geraghty Type Contractions in Partially Ordered Metric Spaces

The notion of generalized almost Geraghty type contraction non-self maps in partially ordered metric spaces is introduced, and some new best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

FUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...