jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

The contraction phase of the T cell response is a poorly understood period after the resolution of infection when virus-specific effector cells decline in number and memory cells emerge with increased frequencies. CD8(+) T cells plummet in number and quickly reach stable levels of memory following acute lymphocytic choriomeningitis virus infection in mice. In contrast, virus-specific CD4(+) T c...

Keywords: System of nonlinear integral equations Step method Picard operators Generalized fibre contraction principle a b s t r a c t Using the step method, we study the following system of integral equations from biomathematics xðtÞ ¼ gðt; xðtÞ; xðt À sÞÞ þ Z t tÀs f ðs; xðsÞÞds; t 2 ½a; bŠ; s > 0 and we prove the existence, uniqueness and the convergence of the successive approximation sequen...

IL-7 is integral to the generation and maintenance of CD8(+) T cell memory, and insufficient IL-7 is believed to limit survival and the persistence of memory CD8(+) T cells. Here, we show that during the mouse T cell response to lymphocytic choriomeningitis virus, IL-7 enhanced the number of memory CD8(+) T cells when its administration was restricted to the contraction phase of the response. L...

and Applied Analysis 3 Definition 2.3 see 16 . Let X,F, T be a probabilistic metric space. A mapping f : X → X is said to be a Sehgal contraction or B-contraction if the following relation holds: Ff p f q kt ≥ Fpq t , ( p, q ∈ X, t > 0. 2.1 Theorem 2.4 see 17 . Let X,F, T be a complete probabilistic metric space with T of Hadžić-type and f : X → X be a B-contraction. Then f has a fixed point if...

BACKGROUND CD8(+) T cell responses develop rapidly during infection and are swiftly reduced during contraction, wherein >90% of primed CD8(+) T cells are eliminated. The role of apoptotic mechanisms in controlling this rapid proliferation and contraction of CD8(+) T cells remains unclear. Surprisingly, evidence has shown non-apoptotic activation of caspase-3 to occur during in vitro T-cell prol...

CD8(+) T cells provide protection against pathogens and cancer. After encountering a pathogenic antigen, CD8(+) T cells undergo a triphasic program of rapid proliferation, contraction, and memory formation. Most (∼90-95%) CD8(+) T cells die after vigorous proliferation in the T cell contraction phase, yet the mechanism that triggers apoptotic T cell death remains elusive. This study tested the ...

One of the main methods of examining non-normal operators, acting on Hilbert spaces, is the theory of contractions. This area of operator theory was developed by Béla Sz.-Nagy and Ciprian Foias from the dilation theorem of Sz.-Nagy. Sz.-Nagy and Foias classi ed the contractions according to their asymptotic behaviour. They got strong structural results in the case when the contraction and its a...

If (X, d) is a complete metric space and T : X → X is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of T starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader...