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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 4

ON VARIOUS TYPES OF COMPATIBLE MAPS AND COMMON FIXED POINT THEOREMS FOR NON-CONTINUOUS MAPS

M.R. SINGH
Y. Mahendra SINGH
Pages
503–513
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Math. 32(1) (1999), 157–163, 1999), and others.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Concepts of S- and A- compatible of type (E), S- and A- reciprocally continuous are introduced.
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Key Findings & Data:Math. 1 (14), 261–270, 2005), X.
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Conclusion & Impact:Math. 32(1) (1999), 157–163, 1999), and others.
🔬Design:Research Article
📍Scope:2005 Verileri
⚙️Variables:Compatible maps · Compatible of type (E) · S- and A-compatible of type (E)

Abstract

Concepts of S- and A- compatible of type (E), S- and A- reciprocally continuous are introduced. In this paper, we give a brief discussion on various types of compatible maps and obtain some common fixed point theorems for non-continuous self maps on a metric space. Here the utility of the newly introduced maps viz. S- compatible of type (E) and S- reciprocally continuous (one sided) in lieu of continuity is shown. Our results improve, generalize or extend the results of H. Bouhadjera (General common fixed point theorem for compatible mappings of type (C), Sarajevo J. Math. 1 (14), 261–270, 2005), X. P. Ding (Some common fixed point theorems of commuting mappings II, Math.Seminar Note 11, 301–305, 1983), M. L. Diviccaro and S. Sessa (Some remarks on common fixed points of four mappings, Jnanabha 15, 139– 149, 1985), G. Jungck (Compatible mappings and common fixed points (2), Internat. J. Math. & Math. Sci. 11 (2), 285–288, 1988), S.M. Kang, Y. J. Cho and G. Jungck (Common fixed points of compatible mappings, Internat. J. Math. & Math. Sci. 13 (1), 61–66, 1990), V. Popa (Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math. 32(1) (1999), 157–163, 1999), and others.

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Cite This Article

SINGH, M., SINGH, Y. M. (2022). ON VARIOUS TYPES OF COMPATIBLE MAPS AND COMMON FIXED POINT THEOREMS FOR NON-CONTINUOUS MAPS. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 4, 503–513. https://ajindex.com/articles/530598

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