A pair of non-self mappings and their fixed point satisfying integral type contraction condition in convex spaces
Resumo
A common xed point theorem is proved for a pair of non-self mappings
by using contraction condition of integral type on non-empty closed subset K of
a metrically convex metric space X: Result generalizing and unifying the previous
results due to Branciari [2], Ciric [4], Rhoades [19], Khan [12, 13] and others.
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Referências
N. A. Assad and W. A. Kirk, Fixed point theorems for set valued mappings of contractive type, Pacific J. Math. 43(3)(1972), 553-562.
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 9(29)(2002), 531 - 536.
Lj. B. Ciric and J. S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Annal. Appl. 314(2002), 488 - 499.
Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45(1974), 267-273.
O. Hadzic, On coincidence points in convex metric spaces, Univ. U. Novom. Sadu. Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 19(2)(1986), 233-240.
O. Hadzic and Lj. Gajic, Coincidence points for set-valued mappings in convex metric spaces, Univ. U. Novom. Sadu. Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 16(1)(1986), 13-240.
M. Imdad and L. Khan, Fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces, Fixed Point Theory Appl. 3(2005), 1281-294.
M. Imdad and L. Khan, Rhoades type fixed point theorems for two hybrid pairs of mappings in metrically convex spaces, Nonlinear Analysis Hybrid Systems, 4(2010) 79-84.
M. Imdad, L. Khan and D. R. Sahu, Common fixed point theorems for two pairs of non-self mappings, J. Appl. Math. Computing, 21(1-2)(2006), 269 - 287.
G. Jungck, Common fixed point for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4(2) (1996), 199-215.
L. Khan, Fixed point theorem for weakly contractive maps in metrically convex spaces under C class function, Nonlinear Functional Analysis and Applications, 25(1)(2020), 153 - 160.
L. Khan, Fixed point theorem for non-self mappings satisfying contraction condition of integral type in metrically convex spaces, Proceedings of Institute Applied Mathematics, 10(1)(2021), 16 - 24. 8 Ladlay Khan
L. Khan, Fixed point theorem for non-self mappings satisfying generalized contraction condition of integral type in metrically convex spaces, Italian Journal of Pure and Applied Mathematics, 48(2022), 733 - 740.
L. Khan and M. Imdad, Rhoades type fixed point theorems for two hybrid pairs of mappings in metrically convex spaces, Applied Mathematics and Computation, 218(2012), 8861 - 8868.
L. Khan and M. Imdad, Meir and Keeler type fixed point theorem for set-valued generalized contractions in metrically convex spaces, Thai Journal of Mathematics, 10(3)(2012), 473 - 480.
L. Khan and M. Imdad, Fixed point theorems for two hybrid pairs of multi-valued non-self mappings in metrically convex spaces, Nonlinear Analysis Forum, 21(2)(2016), 43 - 54.
S. B. Nadler, Multi-valued contraction mappings, Pacefic J. Math. 30(2)(1969), 475 - 488.
B. E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23(4)(1978), 457-459.
B. E. Rhoades, Two fixed point theorems for mappings satisfying a contractive condition of integral type, Int. J. Math. Math. Sci. 63(2003), 4007 - 4013.
S. Sessa, On a weak commutativity condition in fixed point considerations, Publ. Inst. Math. 32(4-6)(1982), 149 - 153.
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