• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.497-512
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• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.387-395
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• 2015

We investigate conditions under which a holomorphic self-map of the unit disk induces a bounded composition operator and study some properties of the composition operator from the Bloch-type spaces into a generalization of the Bloch-type spaces.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.379-385
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• 2008

Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.407-416
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• 1999

In this paper we give some sufficient conditions for the existence and uniqueness of a continuous for the existence and uniqueness of a continuous slution of the system of Urysohn-Volterra equation with hysteresis.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.77-90
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• 2000

In this paper, we will establish the existence theorem of the operator valued function space integral over paths in abstract Wiener space under the general conditions rather than the known conditions.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.427-436
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• 1997

In the present paper, we invetigate some argument properties of certain analytic functions and the integral preserving properties in a sector. Our results include several previous results as special cases.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.773-784
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• 2022

The purpose of the present paper is to estimate some real parts for certain analytic functions with some applications in connection with certain integral operators and geometric properties. Also we extend some known results as special cases of main results presented here.