In this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces.MSC: 46T99; 46N40; 47H10; 54H25

In this paper, we investigate Dragomir and Gosa type inequalities in the setting of b-metric spaces. As an application, we consider some inequalities in b-normed spaces. We prove that the inequalities admit geometrical interpretation.

The aim of the paper is to introduce the concept of new hybrid contractions that combine Jaggi hybrid type contractions and Suzuki type contractions with w -orbital admissible. We investigate the existence and uniqueness of such new hybrid contractions in theorems and results. Further, an illustrated example is given. With the results of this study, we generalize several well-known results in the recent fixed point literature.

<abstract><p>In this manuscript, a novel general family of contraction, called hybrid-interpolative Reich-Istr$ \breve{a}ţ $escu-type $ (G $-$ \alpha $-$ \mu) $-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other well-known results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations.</p></abstract>

In this research article, fixed point theory is beautifully combined with fuzzy set theory. Two fuzzy fixed point theorems of L-fuzzy mappings are established and proved for two different contractive type conditions in the scenario of complete b-metric space. In order to give the strength of these results, nontrivial supportive examples for both results are also provided. The notion of L-fuzzy mappings is a generalized form of fuzzy mappings as well as multivalued mappings. In this approach, our results provide uniqueness, extension, and successive generalizations of many valuable recent and conventional results existing in the literature.