On some fixed point results for (s, p, α)-contractive mappings in b-metric-like spaces and applications to integral equations

Abstract

In this work, we introduce the notions of (s, p, α)-quasi-contractions and (s, p)-weak contractions and deduce some fixed point results concerning such contractions, in the setting of b-metric-like spaces. Our results extend and generalize some recent known results in literature to more general metric spaces. Moreover, some examples and applications support the results.

Common Fixed Point Results for GeneralizedαspContractive Mappings and Applications

“…Remark 35. Our results generalize, extend, and improve the results appearing in the literature [3,7,10,12,16,21,26,28,29,[31][32][33][34]. It is clear that several more corresponding results can be derived by our main theorems by choosing constant and the mappings , , in a suitable way.…”

“…Lemma 14 (see [29]). Let ( , ) be a complete -metric-like space with parameter ≥ 1 and let { } be a sequence such that…”

Generalized Contractive Mappings and Related Results in b-Metric Like Spaces with an Application

“…Therefore, all the axioms of Corollary 1 are satisfied by taking the coefficient q " 2, and function φpκq " p1´µ s qκ, where µ s P p0, 1q and β " 1 3 . Hence the mapping T has a unique fixed point in X, which is a solution of the integral equation in (27).…”

Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

“…It is clear that each metric-like space, i.e., each partial b-metric space, is a b-metric-like space, while the converse is not true. For more such examples and details see [1,2,[5][6][7][15][16][17][18][19][20][21][22][23][24][25][26][27]. Moreover, for various metrics in the context of the complex domain see [28,29].…”