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Saluja, G. S.

Convergence Theorems of Finite Steps Iterative Sequences with Mean Errors for Generalized Asymptotically Quasi-Nonexpansive Mappings

Convergence Theorems for Two Asymptotically Nonexpansive Non-self Mappings in Uniformly Convex Banach Spaces

Abstract Views :167 | PDF Views:0

Authors

G. S. Saluja ¹

Affiliations
1 Department of Mathematics and I. T., Govt. N. P. G. College of Science, Raipur (C. G.), IN

Source

The Journal of the Indian Mathematical Society, Vol 81, No 3-4 (2014), Pagination: 369-385

Abstract

Let K be a nonempty closed convex non expansive retract of a uniformly convex Banach space E with P as a non expansive retraction. Let T₁, T₂: K → E be two asymptotically non expansive non-self mappings with sequences {k_n }, {h_n } ⊂[1,(∞) such that Σ^∞_n=1(k_n h_n -1) < ∞ and F = F(T₁) ∩ F(T₂) = {x E K : T₁x = T₂x = x}≠ Φ . Let {x_n}^∞n=1 be the sequence generated iteratively by x_l ∈ K and x_n+1 = P(a_nx_n + b_nT₁ (PT₁ )^n-1y_n + c_nl_n ) ∀_n ≥1 y_n = P(ā_n x_n + b_n T_n (PT₂ )^n-1x_n + c_nm_n ),∀_n ≥1 where {l_n }, {m_n} are bounded sequences, a_n+b_n +c_n = 1 = ā_n +b_n +c_n,0 ≤ a_n +b_n +c_n, ā_n +b_n +c_n ≤ 1, ∀_n ∈ N, Σ^∞_n=1 c_n < ∞ and Σ^∞_n=1 b_nc_n <∞ . If T₁ is completely continuous or T₁ and T₂ satisfy condition (A'), then {x_n} converges strongly to a point in F = F(T₁) ∩ F(T₂). Also if E satisfies Opial's condition or the dual E* of E has the Kedec-Klee property, then {x_n} converges weakly to a point in F.

Keywords

Asymptotically Non Expansive Nonself Mappings, Common Fixed Point, the Modified Ishikawa Iterative Sequence with Errors for Non-Self Maps, Uniformly Convex Banach Space, Strong Convergence, Weak Convergence.

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Some Fixed Point Theorems Under Contractive Type Conditions in Complex Valued Metric Spaces

Abstract Views :270 | PDF Views:1

Authors

G. S. Saluja

Source

The Journal of the Indian Mathematical Society, Vol 84, No 1-2 (2017), Pagination: 96-108

Abstract

The purpose of this paper is to establish some fixed point and common fixed point theorems under contractive type conditions involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize some previous works from the existing literature.

Keywords

Fixed Point, Common Fixed Point, Contractive Type Condition, Complex Valued Metric Space.

Full Text

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Some Fixed Point Results in Partial Metric Spaces Under Contractive Type Mappings

Abstract Views :413 | PDF Views:0

Authors

G. S. Saluja ¹

Affiliations
1 Department of Mathematics, Govt. K. P. G. College Jagdalpur, Jagdalpur - 494001 (Chhattisgarh), IN

Source

The Journal of the Indian Mathematical Society, Vol 87, No 3-4 (2020), Pagination: 219–230

Abstract

In this paper, we establish some fixed point theorems and a coincidence point theorem for contractive type mappings in the framework of complete partial metric spaces and give some examples in support of our results. The results presented in this paper extend and generalize several results from the existing literature.

Keywords

Fixed Point, Contractive Type Mapping, Partial Metric Space.

Full Text

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