Some common fixed point results in ordered partial b-metric spaces

Abstract

In this paper, we introduce a modified version of ordered partial b-metric spaces. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Using this lemma, we prove some fixed point and common fixed point results for (ψ , ϕ)-weakly contractive mappings in the setup of ordered partial b-metric spaces.Finally, examples are presented to verify the effectiveness and applicability of our main results. MSC: 47H10; 54H25

Fixed point results in generalized metric spaces without Hausdorff property

“…We conclude by citing some additional recent references concerned with extensions of the mentioned results to some other types of spaces [42][43][44][45].…”

Some new coupled fixed point theorems in ordered partial b -metric spaces

“…By combining these, Shukla [26] introduced a new generalization of metric space called partial b-metric space which was paid widespread attention immediately. Also, in [19] a modified version of partial b-metric space was introduced and many useful lemmas could be proved right away. Since then, several authors obtained more helpful results in this space [10,19].…”

“…Also, in [19] a modified version of partial b-metric space was introduced and many useful lemmas could be proved right away. Since then, several authors obtained more helpful results in this space [10,19].…”

Resolving systems of nonlinear integral equations via C-class functions

“…In Czerwik (1993) and Czerwik (1998) extended many results related to the bmetric spaces. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric spaces (Akkouchi, 2011;Aydi et al, 2012;Boriceanu, 2009;Boriceanu et al, 2010;Bota et al, 2011;Hussain & Shah, 2011;Olatinwo, 2008;Huang et al, 2015;Mustafa et al, 2013;Mustafa et al, 2014;Ansari et al, 2014;Aghajani et al, 2014).…”