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MONOTONE GENERALIZED CONTRACTIONS IN ORDERED METRIC SPACES
Alam, Aftab,Imdad, Mohammad Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and $Rodr{\acute{i}}guez$-$L{\acute{o}}pez$ (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.
Monotone generalized contractions in ordered metric spaces
Aftab Alam,Mohammad Imdad 대한수학회 2016 대한수학회보 Vol.53 No.1
In this paper, we prove some existence and uniqueness results on coincidence points for $g$-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. {\bf 132} (2004), no. 5, 1435--1443) and Nieto and Rodr\'{\i}guez-L\'{o}pez (Acta Math. Sin. {\bf 23} (2007), no. 12, 2205--2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.
REMARKS ON CERTAIN NOTED COINCIDENCE THEOREMS: A UNIFYING AND ENRICHING APPROACH
Aftab Alam,Mohd. Hasan,Mohammad Imdad 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.5
In this paper, we unify and enrich the well-known classical metrical coincidence theorems on a complete metric space due to Machuca, Goebel and Jungck. We further extend our newly proved results on a subspace Y of metric space X, wherein X need not be complete. Finally, we slightly modify the existing results involving (E.A)-property and (CLR_g)-property and apply these results to deduce our coincidence and common fixed point theorems.