Z. Opial

3.1k total citations · 1 hit paper
35 papers, 2.2k citations indexed

About

Z. Opial is a scholar working on Numerical Analysis, Computational Theory and Mathematics and Applied Mathematics. According to data from OpenAlex, Z. Opial has authored 35 papers receiving a total of 2.2k indexed citations (citations by other indexed papers that have themselves been cited), including 16 papers in Numerical Analysis, 15 papers in Computational Theory and Mathematics and 14 papers in Applied Mathematics. Recurrent topics in Z. Opial's work include Differential Equations and Numerical Methods (12 papers), Advanced Mathematical Modeling in Engineering (12 papers) and Nonlinear Differential Equations Analysis (10 papers). Z. Opial is often cited by papers focused on Differential Equations and Numerical Methods (12 papers), Advanced Mathematical Modeling in Engineering (12 papers) and Nonlinear Differential Equations Analysis (10 papers). Z. Opial collaborates with scholars based in Poland and United States. Z. Opial's co-authors include Andrzej Lasota, Czesław Olech and Marek Kuczma and has published in prestigious journals such as Journal of Differential Equations, Bulletin of the American Mathematical Society and Colloquium Mathematicum.

In The Last Decade

Z. Opial

33 papers receiving 1.8k citations

Hit Papers

Weak convergence of the sequence of successive approximat... 1967 2026 1986 2006 1967 500 1000 1.5k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Weak convergence of the sequence of successive approximations for nonexpansive mappings
    1967 1.7k citations Z. Opial profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Z. Opial Poland 13 1.6k 1.3k 1.1k 604 386 35 2.2k
W. V. Petryshyn United States 26 2.3k 1.4× 1.3k 1.0× 1.7k 1.6× 1.1k 1.8× 598 1.5× 87 3.2k
W. Robert Mann United States 6 1.5k 0.9× 1.1k 0.9× 1.2k 1.1× 264 0.4× 259 0.7× 11 1.9k
Ronald E. Bruck United States 18 1.6k 1.0× 864 0.7× 1.1k 1.0× 442 0.7× 436 1.1× 27 1.8k
Jean‐Paul Penot France 28 2.3k 1.4× 1.2k 1.0× 886 0.8× 916 1.5× 554 1.4× 144 2.7k
A. D. Ioffe Israel 26 2.3k 1.4× 1.2k 1.0× 849 0.8× 782 1.3× 580 1.5× 87 2.6k
Kazimierz Goebel Poland 8 2.5k 1.6× 1.5k 1.2× 1.9k 1.8× 672 1.1× 585 1.5× 19 3.0k
Frank Deutsch United States 23 955 0.6× 643 0.5× 452 0.4× 270 0.4× 435 1.1× 63 1.6k
Lionel Thibault France 28 2.2k 1.4× 948 0.8× 653 0.6× 826 1.4× 667 1.7× 132 2.5k
Zeev Nehari United States 26 693 0.4× 930 0.7× 412 0.4× 1.8k 2.9× 569 1.5× 69 2.4k
Sam B. Nadler United States 15 1.2k 0.7× 264 0.2× 2.7k 2.6× 804 1.3× 854 2.2× 81 3.4k

Countries citing papers authored by Z. Opial

Since Specialization
Citations

This map shows the geographic impact of Z. Opial's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Z. Opial with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Z. Opial more than expected).

Fields of papers citing papers by Z. Opial

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Z. Opial. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Z. Opial. The network helps show where Z. Opial may publish in the future.

Co-authorship network of co-authors of Z. Opial

This figure shows the co-authorship network connecting the top 25 collaborators of Z. Opial. A scholar is included among the top collaborators of Z. Opial based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Z. Opial. Z. Opial is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Opial, Z.. (1967). Linear problems for systems of nonlinear differential equations. Journal of Differential Equations. 3(4). 580–594. 42 indexed citations
2.
Lasota, Andrzej & Z. Opial. (1967). On the existence and uniqueness of solutions of a boundary value problem for an ordinary second-order differential equation. Colloquium Mathematicum. 18(1). 1–5. 44 indexed citations
3.
Opial, Z.. (1967). Lecture notes on nonexpansive and monotone mappings in Banach spaces. NASA Technical Reports Server (NASA). 13 indexed citations
4.
Lasota, Andrzej & Z. Opial. (1967). Sur la dépendance continue des solutions des équations différentielles ordinaires de leurs seconds membres et des conditions aux limites. Annales Polonici Mathematici. 19(1). 13–36. 7 indexed citations
5.
Opial, Z.. (1967). Continuous parameter dependence in linear systems of differential equations. Journal of Differential Equations. 3(4). 571–579. 21 indexed citations
6.
Opial, Z.. (1967). On a theorem of O. Aramă. Journal of Differential Equations. 3(1). 88–91. 22 indexed citations
7.
Lasota, Andrzej & Z. Opial. (1964). Sur les solutions périodiques des équations différentielles ordinaires. Annales Polonici Mathematici. 16(1). 69–94. 48 indexed citations
8.
Opial, Z.. (1961). Sur l'existence des solutions périodiques de l'équation différentielle x'' + f(x,x')x' + g(x) = p(t). Annales Polonici Mathematici. 11(2). 149–159. 8 indexed citations
9.
Opial, Z.. (1961). Sur la limitation des dérivées des solutions bornées d'un système d'équations différentielles du second ordre. Annales Polonici Mathematici. 10(1). 73–79. 2 indexed citations
10.
Opial, Z.. (1960). Sur les solutions périodiques et presque-périodiques de l'équation différentielle x'' + kf(x)x' + g(x) = kp(t). Annales Polonici Mathematici. 7(3). 309–319. 7 indexed citations
11.
Opial, Z.. (1960). Sur la stabilité asymptotique des solutions d'un système d'équations différentielles. Annales Polonici Mathematici. 7(3). 259–267. 8 indexed citations
12.
Opial, Z.. (1960). Sur l'équation différentielle ordinaire du premier ordre dont le second membre satisfait aux conditions de Carathéodory. Annales Polonici Mathematici. 8(1). 23–28. 5 indexed citations
13.
14.
Opial, Z.. (1960). Sur une équation différentielle non linéaire du second ordre. Annales Polonici Mathematici. 8(1). 65–69. 6 indexed citations
15.
Opial, Z.. (1960). Démonstration d'un théorème de N. Levinson et C. Langenhop. Annales Polonici Mathematici. 7(3). 241–246. 7 indexed citations
16.
Kuczma, Marek, et al.. (1959). La courbure d'une courbe plane et l'existence d'une asymptote. Annales Polonici Mathematici. 5(3). 275–283.
17.
Opial, Z.. (1958). Sur un théorème de A. Filippoff. Annales Polonici Mathematici. 5(1). 67–75. 12 indexed citations
18.
Opial, Z.. (1958). Sur l'équation différentielle u'' + a(t)u = 0. Annales Polonici Mathematici. 5(1). 77–93. 7 indexed citations
19.
Opial, Z.. (1957). Sur un système d'inégalités intégrales. Annales Polonici Mathematici. 3(2). 200–209. 9 indexed citations
20.
Opial, Z., et al.. (1955). Un lemme sur les polynômes de Lagrange. Annales Polonici Mathematici. 2(1). 73–76. 1 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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