TY - JOUR
T1 - F-convex contraction via admissible mapping and related fixed point theorems with an application
AU - Singh, Y. Mahendra
AU - Khan, Mohammad Saeed
AU - Kang, Shin Min
N1 - Publisher Copyright:
© 2018 by the authors.
PY - 2018/6/20
Y1 - 2018/6/20
N2 - In this paper, we introduce F-convex contraction via admissible mapping in the sense of Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94 (2012), 6 pages] which extends convex contraction mapping of type-2 of Istrăţescu [Some fixed point theorems for convex contraction mappings and convex non-expansive mappings (I), Libertas Mathematica, 1(1981), 151-163] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.
AB - In this paper, we introduce F-convex contraction via admissible mapping in the sense of Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94 (2012), 6 pages] which extends convex contraction mapping of type-2 of Istrăţescu [Some fixed point theorems for convex contraction mappings and convex non-expansive mappings (I), Libertas Mathematica, 1(1981), 151-163] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.
KW - Fixed point
KW - Non-linear Fredholm integral equation
KW - α-admissibleαF-contraction
KW - α-F-convex contraction
KW - α-admissible mapping
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U2 - 10.3390/math6060105
DO - 10.3390/math6060105
M3 - Article
AN - SCOPUS:85048840894
SN - 2227-7390
VL - 6
JO - Mathematics
JF - Mathematics
IS - 6
M1 - 105
ER -