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Ravi P. Agarwal ¹, Maryam A. Alghamdi ², Donal O'Regan ³, Naseer Shahzad ⁴

Affiliations
1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363 - 8202, US
2 Department of Mathematics, King Abdulaziz University, Sciences Faculty for Girls, P.O. Box 4087, Jeddah 21491, SA
3 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, IE
4 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, SA

Abstract

In this paper, we present fixed point theory for weakly Kannan mappings that satisfy cyclical conditions on complete metric spaces.

Keywords

Fixed Point, Cyclic Map, Kannan Map, Weakly Kannan Map, Metric Space.

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Said R. Grace ¹, Ravi P. Agarwal ², Donal O'regan ³

Affiliations
1 Department of Engg. Mathematics, Cairo University, Orman, Giza 12221, EG
2 Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, SA
3 Department of Maths., National University of Ireland, Galway, IE

Abstract

Oscillation criteria are established for second order dynamic inclusions of the form (ay^Δ)^Δ(t)∈ F(t, y^σ(t)) for a.e. t≥t₀≥0, t₀ ∈ T: We note that the results of this paper are new even in the single-valued case.

Keywords

Oscillation, Superlinear, Sublinear, Dynamic Inclusions.

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