In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Samet (Fixed Point Theory Appl. 2015:33, 2015.MSC: Primary 47H10; secondary 54H25
In this paper, we present some fixed point results for generalized θ‐ϕ‐contraction in the framework of α,η−compete rectangular b‐metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.
In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of
g
-interpolative Hardy–Rogers type contractions in
b
-metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.
In this research paper, we have set some related fixed point results for generalized weakly contractive mappings defined in partially ordered complete
b
-metric spaces. Our results are an extension of previous authors who have already worked on fixed point theory in
b
-metric spaces. We state some examples and one sample of the application of the obtained results in integral equations, which support our results.
We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.
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